$$24\cdot\dfrac{x^3}{25}y^515\dfrac{y^2}{8}x^2=\dfrac{360x^5y^7}{200}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}24 \cdot \frac{x^3}{25}y^515\frac{y^2}{8}x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24x^3}{25}y^5\frac{15y^2}{8}x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{24x^3y^5}{25}\frac{15x^2y^2}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{360x^5y^7}{200}\end{aligned} $$ | |
| ① | Multiply $24$ by $ \dfrac{x^3}{25} $ to get $ \dfrac{ 24x^3 }{ 25 } $. Step 1: Write $ 24 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 24 \cdot \frac{x^3}{25} & \xlongequal{\text{Step 1}} \frac{24}{\color{red}{1}} \cdot \frac{x^3}{25} \xlongequal{\text{Step 2}} \frac{ 24 \cdot x^3 }{ 1 \cdot 25 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 24x^3 }{ 25 } \end{aligned} $$ |
| ② | Multiply $15$ by $ \dfrac{y^2}{8} $ to get $ \dfrac{ 15y^2 }{ 8 } $. Step 1: Write $ 15 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 15 \cdot \frac{y^2}{8} & \xlongequal{\text{Step 1}} \frac{15}{\color{red}{1}} \cdot \frac{y^2}{8} \xlongequal{\text{Step 2}} \frac{ 15 \cdot y^2 }{ 1 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15y^2 }{ 8 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{24x^3}{25} $ by $ y^5 $ to get $ \dfrac{ 24x^3y^5 }{ 25 } $. Step 1: Write $ y^5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{24x^3}{25} \cdot y^5 & \xlongequal{\text{Step 1}} \frac{24x^3}{25} \cdot \frac{y^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 24x^3 \cdot y^5 }{ 25 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 24x^3y^5 }{ 25 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{15y^2}{8} $ by $ x^2 $ to get $ \dfrac{ 15x^2y^2 }{ 8 } $. Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{15y^2}{8} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{15y^2}{8} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 15y^2 \cdot x^2 }{ 8 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15x^2y^2 }{ 8 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{24x^3y^5}{25} $ by $ \dfrac{15x^2y^2}{8} $ to get $ \dfrac{ 360x^5y^7 }{ 200 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{24x^3y^5}{25} \cdot \frac{15x^2y^2}{8} & \xlongequal{\text{Step 1}} \frac{ 24x^3y^5 \cdot 15x^2y^2 }{ 25 \cdot 8 } \xlongequal{\text{Step 2}} \frac{ 360x^5y^7 }{ 200 } \end{aligned} $$ |